Riemann \(\Xi (2z)\)  function can be expressed as a Fourier transformation  [1]}, [2]}, [3]}:
\(\Xi (2z)=\int _{-\infty }^{\infty }\Phi (t)\exp (izt){\rm d}u=2\int _0^{\infty }\Phi (t)\cos (zt){\rm d}t,\) 
